Rule of 72 Calculator

The Rule of 72 estimates doubling time for compound growth: years to double ≈ 72 ÷ annual rate (in percent). At 8% it's 9 years; at 12% it's 6 years. The exact formula is ln(2)/ln(1+r), so the rule is most accurate near 8% and drifts at the extremes.

The calculator returns both the rule estimate and the exact value, plus the inverse — what return doubles your money in N years.

The Rule of 72 derives from the doubling-time formula ln(2)/ln(1+r). A Taylor expansion of ln(1+r) around r=0 gives r − r²/2 + r³/3 − …; for small r, ln(1+r) ≈ r, so doubling time ≈ ln(2)/r ≈ 0.693/r. To work in percent rather than decimals, multiply by 100: doubling time ≈ 69.3/rate. The choice of 72 over 69.3 is for divisibility — 72 has many integer divisors (2, 3, 4, 6, 8, 9, 12) making mental math easier. The error is small in the typical investment range (5–15%); at extremes the rule drifts. At 1% rate the rule says 72 years versus exact 69.66 (3% off); at 25% it says 2.88 years versus exact 3.11 (7% off). For continuous compounding, the rule of 69.3 is exact; for discrete annual compounding, 72 is closer to optimal across normal rates.

A worked example: a stock index returning a long-term average of 10% nominal would double approximately every 7.2 years by the rule. Exact: ln(2)/ln(1.10) = 7.27 years. Adjusting for 3% inflation gives 7% real return, doubling every 10.3 years (rule) or 10.24 years (exact). Over 30 years a 10% nominal return goes through roughly four doublings (29 years), turning $10,000 into $160,000. Adjusted to real terms (7%), it goes through three doublings, equivalent to $80,000 in present-day purchasing power.

Limitations: the rule assumes compound growth with a fixed rate. Stock returns are highly variable year to year; the average return over decades doesn't mean every year delivers it. Sequence-of-returns risk — getting bad years early — can deviate substantially from the rule's prediction. The rule doesn't account for taxes, fees, or contributions/withdrawals; for those, use the full FV formula or a financial calculator. Inflation matters: nominal versus real returns produce very different doubling times for the same investment.